I suspect your truck will be overloaded, but OP has not furnished enough information to determine that.
First learn what the terms mean.
GVWR Gross Vehicle Weight Rating: The most the truck, fuel, passengers, cargo and trailer tongue can weigh.
GAWR Gross Axle Weight Rating: The most weight that can be on one axle.
GCWR Gross Combined Weight Rating: The most the loaded truck and camper can weigh
Payload: The most that all the passengers and cargo in the truck can weigh. This is equal to the GVWR minus the weight of the truck with a full tank of fuel.
Tow Rating or Max Trailer Weight: GCWR minus the weight of the truck.
Find the weight sticker from the edge of the door in the truck.
My truck weighed 7100 (GVWR) - 1607 (payload) = 5493 lbs.
Find the weight sticker on the camper.
In this case, the camper from the factory weighed 7765 (GVWR) - 2470 (payload) = 5025 (dry weight)
This usually does not include batteries, propane or water.
Find the weight sticker underneath the hitch receiver under the back of the truck.
On my truck, the max tongue weight is 500 lbs. without a weight distribution hitch (WDH), and 1050 with one.
When I loaded my toy hauler with water, propane, two batteries, one dirt bike, tools, spares, food, clothes, etc. it weighed 6640 lbs.
With just one person, a tonneau cover, spray in liner and a few tools in the truck, it weighed 5860 lbs., including 367 lbs. of passengers, cargo and after market equipment. The tongue on the 6640 lb. trailer weighs 900 lbs.
The WDH transferred 140 lbs. of that 900 to the trailer axles, leaving the truck weighing 6640 lbs. My truck has a "tow rating" of 9800 lbs. With a trailer weighing 6640 lbs., it has used up 71% of that 1607 lb. payload. It is just 460 lbs. under the GVWR limit. Two hefty passengers, or three skinny ones will load it to the limit.
I know the aluminum trucks generally have a higher payload, but I fear your trailer will overload your truck. It's not so much what it can TOW, but what it can HAUL. Most trucks run out of GVWR before they run out of GCWR.